径向基函数

径向基函数（英語：Radial basis function，缩写为RBF）是一个取值仅依赖于到原点距离的实值函数（英语：Real-valued function），即。此外，也可以按到某一中心点c的距离来定义， 即。任一满足的函数都可称作径向函数。其中，范数一般为欧几里得距离，不过亦可使用其他距离函数。

可以用于许多向函基数的和来逼近某一给定的函数。这一逼近的过程可看作是一个简单的神经网络。[1][2]此外在机器学习中，径向基函数还被用作支持向量机的核函数。

类型

常见的径向基函数包括（定义）：

  • 多二次函数（multiquadric）：
  • 逆二次函数（inverse quadratic）：
  • 逆多二次函数（inverse multiquadric）：
  • 多重调和样条（polyharmonic spline）：
  • 薄板样条（thin plate spline，为多重调和样条的特例）：

参见

参考文献

  1. ^ Radial Basis Function networks 互联网档案馆的存檔，存档日期2014-04-23.
  2. ^ Broomhead, David H.; Lowe, David. Multivariable Functional Interpolation and Adaptive Networks (PDF). Complex Systems. 1988, 2: 321–355. （原始内容 (PDF)存档于2014-07-14）. 

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